Question

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): critical reading-502; mathematics-515; writing-494; Assume that the population standard deviation on each part of the test is = 100.. What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)?

Answer 1

A. P(492 < x-bar < 512) 

z = (492-502)/100/√90 

z = -0.95 is 0.1711 

z = (512-502)/100/√90 

z = 0.95 is 0.8289 

b. P(505 < x-bar < 525) 

z = (505-515)/100/ √90 

z = -0.95 

z = (525-515)/100/ √90 

z = 0.95 

P(-0.95< z < 0.95) = 0.6578 

P(-0.95< z < 0.95) = 0.6578 

c. P(484 < x-bar < 504) 

z = (484-494)/100/√100 

z = -1 is 0.1587 

z = (504-494)/100/√100 

z = 1 is 0.8413 

P(-1< z <1) = 0.6826